Well, we certainly have a lively, energetic, and committed crew out onthe Geometry Forum! Possibly a little trigger happy though ... Ithink folks have assumed the worst in response to queries from me andBill Berlinghoff about defining "angle". We are NOT taking anaxiomatic approach to geometry nor are we contemplating most of theother crimes suggested. In trying to defend ourselves, I think we'vecome out looking much more conservative than we are. We just wantedto know how people are approaching the idea of angle.

Maybe a non-geometric example would be less incendiary. In our ninthgrade materials we define "mean absolute deviation" as the mean of theabsolute value of the deviations from the mean. (Our treatment thereis not so curt.) Now I have seen people argue that the thing to lookat is the deviations from the MEDIAN, or that we should look at themedian of the deviations. Now whatever the pros and cons of thesepositions might be, and however we might present the material tostudents, I think we need to be clear in our own mind what thedifferent definitions are and be consistent in our own usage so thatwe do not have MAD meaning different things on different pages. Also,if we have not considered various alternative definitions, or evenconceived of their existence, we can't initiate a very intelligentdialog with students on these alternatives. Finally, if one of thedefinitions is overwhelmingly accepted as "correct', and the othersare considered misunderstandings or errors, then we should know thattoo.